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2 votes
0 answers
175 views

Expository material on the Gromov-Lawson surgery theorem

I am looking for an expository text on the paper "The classification of simply connected manifolds of positive scalar curvature" by Gromov and Lawson, in particular on the proof of Theorem A....
3 votes
1 answer
239 views

A question on the proof of Theorem 1 in Milnor's "Killing Homotopy Groups"

Theorem 1 of Milnor's paper "A procedure for killing homotopy groups of differentiable manifolds" states that two manifolds are in the same cobordism class if and only if they can be ...
7 votes
3 answers
249 views

Normal invariants

I am having a hard time finding examples of computations of normal invariants of surgery theory (or more generally the set of homotopy classes of maps $[X,G/O]$). Does anybody have good references?
23 votes
2 answers
851 views

Classification of fake (quaternionic, octonionic) projective spaces

If $X$ is a closed $n$-manifold, a fake $X$ is another closed manifold homotopy equivalent to $X$. There is some interest in classifying manifolds (up to, say, homeomorphism) homotopy equivalent to a ...
7 votes
0 answers
355 views

Making diffeomorphism of submanifolds boring

This is probably very well known in surgery theory... I'm looking for a modern reference on the following questions (the only one I know is Browder's "Diffeomorphism of 1-connected manifolds"...
10 votes
2 answers
544 views

Obtain 4-manifolds by repeating surgeries of submanifolds in $S^4$

In his paper QFT and Jones Polynomials, Witten states: "It is a not too deep result that every 3-manifold can be obtained from or reduced to $S^3$ (or any other desired 3-manifold) by repeated ...